details

property	value
status	complete
benchmark	random-516.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n086.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	9.59583 seconds
cpu usage	30.7865
user time	29.2284
system time	1.55813
max virtual memory	6.2835352E7
max residence set size	4153052.0

stage attributes

key	value
starexec-result	YES

output

28.80/8.47 YES 30.63/9.12 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 30.63/9.12 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 30.63/9.12 30.63/9.12 30.63/9.12 Termination w.r.t. Q of the given QTRS could be proven: 30.63/9.12 30.63/9.12 (0) QTRS 30.63/9.12 (1) QTRSRRRProof [EQUIVALENT, 39 ms] 30.63/9.12 (2) QTRS 30.63/9.12 (3) DependencyPairsProof [EQUIVALENT, 1 ms] 30.63/9.12 (4) QDP 30.63/9.12 (5) DependencyGraphProof [EQUIVALENT, 1 ms] 30.63/9.12 (6) QDP 30.63/9.12 (7) MRRProof [EQUIVALENT, 34 ms] 30.63/9.12 (8) QDP 30.63/9.12 (9) MRRProof [EQUIVALENT, 5 ms] 30.63/9.12 (10) QDP 30.63/9.12 (11) QDPOrderProof [EQUIVALENT, 51 ms] 30.63/9.12 (12) QDP 30.63/9.12 (13) PisEmptyProof [EQUIVALENT, 0 ms] 30.63/9.12 (14) YES 30.63/9.12 30.63/9.12 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (0) 30.63/9.12 Obligation: 30.63/9.12 Q restricted rewrite system: 30.63/9.12 The TRS R consists of the following rules: 30.63/9.12 30.63/9.12 b(b(a(b(x1)))) -> b(b(b(a(x1)))) 30.63/9.12 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 30.63/9.12 b(a(a(a(x1)))) -> b(b(b(a(x1)))) 30.63/9.12 30.63/9.12 Q is empty. 30.63/9.12 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (1) QTRSRRRProof (EQUIVALENT) 30.63/9.12 Used ordering: 30.63/9.12 Polynomial interpretation [POLO]: 30.63/9.12 30.63/9.12 POL(a(x_1)) = 1 + x_1 30.63/9.12 POL(b(x_1)) = x_1 30.63/9.12 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 30.63/9.12 30.63/9.12 b(a(a(a(x1)))) -> b(b(b(a(x1)))) 30.63/9.12 30.63/9.12 30.63/9.12 30.63/9.12 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (2) 30.63/9.12 Obligation: 30.63/9.12 Q restricted rewrite system: 30.63/9.12 The TRS R consists of the following rules: 30.63/9.12 30.63/9.12 b(b(a(b(x1)))) -> b(b(b(a(x1)))) 30.63/9.12 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 30.63/9.12 30.63/9.12 Q is empty. 30.63/9.12 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (3) DependencyPairsProof (EQUIVALENT) 30.63/9.12 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (4) 30.63/9.12 Obligation: 30.63/9.12 Q DP problem: 30.63/9.12 The TRS P consists of the following rules: 30.63/9.12 30.63/9.12 B(b(a(b(x1)))) -> B(b(b(a(x1)))) 30.63/9.12 B(b(a(b(x1)))) -> B(b(a(x1))) 30.63/9.12 B(b(a(b(x1)))) -> B(a(x1)) 30.63/9.12 B(b(a(a(x1)))) -> B(b(x1)) 30.63/9.12 B(b(a(a(x1)))) -> B(x1) 30.63/9.12 30.63/9.12 The TRS R consists of the following rules: 30.63/9.12 30.63/9.12 b(b(a(b(x1)))) -> b(b(b(a(x1)))) 30.63/9.12 b(b(a(a(x1)))) -> a(a(b(b(x1)))) 30.63/9.12 30.63/9.12 Q is empty. 30.63/9.12 We have to consider all minimal (P,Q,R)-chains. 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (5) DependencyGraphProof (EQUIVALENT) 30.63/9.12 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. 30.63/9.12 ---------------------------------------- 30.63/9.12 30.63/9.12 (6) 30.63/9.12 Obligation: 30.63/9.12 Q DP problem: 30.63/9.12 The TRS P consists of the following rules: 30.63/9.12 30.63/9.12 B(b(a(b(x1)))) -> B(b(a(x1))) popout

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